Caenepeel and Goyvaerts [1]} studied Hom-bialgebras and Hom-Hopf algebras from
a categorical view point, and called them monoidal Hom-bialgebras and monoidal Hom-
Hopf algebras respectively, which are slightly different from the above Hom-bialgebras
and Hom-Hopf algebras.
In [2]}, Chen, Wang and Zhang introduced integrals of monoidal Hom-Hopf algebras and investigated the existence and
uniqueness of integrals for finite-dimensional monoidal Hom-Hopf algebras,
they also applied the integrals to the Maschke type theorem for monoidal
Hom-Hopf algebras controlling the semisimplicity and separability of monoidal
Hom-Hopf algebras.
